Answer
Graph of $
f(x)=x^3+3
$ (blue) and $f^{-1}(x)$ (red, dashed)
Work Step by Step
Substituting the given values of $x$ in the given function, $
f(x)=x^3+3
$, results to
\begin{array}{c|c|c|c}
\text{If }x=-2: & \text{If }x=-1 & \text{If }x=0 & \text{If }x=1
\\\\
f(x)=y=x^3+3 & f(x)=y=x^3+3 & f(x)=y=x^3+3 & f(x)=y=x^3+3
\\
y=(-2)^3+3 & y=(-1)^3+3 & y=0^3+3 & y=1^3+3
\\
y=-8+3 & y=-1+3 & y=0+3 & y=1+3
\\
y=-5 & y=2 & y=3 & y=4
.\end{array}
Tabulating the results above results to the table below.
\begin{array}{c|c}
\hline
x & f(x)
\\\hline
-2 & -5
\\\hline
-1 & 2
\\\hline
0 & 3
\\\hline
1 & 4
\\\hline
\end{array}
Connecting the points $
(-2,-5),(-1,2), (0,3) \text{ and } (1,4)
$ with a curve gives the graph of $
f(x)=x^3+3
$ (blue graph).
Interchanging the $x$ and $y$ coordinates of the points above gives the graph of the inverse function. That is, connecting the points $
(-5,-2),(2,-1), (3,0) \text{ and } (4,1)
$ determines the graph of the inverse function (red dashed line).